Geodesic
Shaken Rogers's Theorem for Homothetic Sections
Canadian mathematical bulletin, Tome 52 (2009) no. 3, pp. 403-406

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DOI

We shall prove the following shaken Rogers's theorem for homothetic sections: Let $K$ and $L$ be strictly convex bodies and suppose that for every plane $H$ through the origin we can choose continuously sections of $K$ and $L$ , parallel to $H$ , which are directly homothetic. Then $K$ and $L$ are directly homothetic.
DOI : 10.4153/CMB-2009-043-8
Mots-clés : 52A15, convex bodies, homothetic bodies, sections and projections, Rogers's Theorem 
Jerónimo-Castro, J.; Montejano, L.; Morales-Amaya, E. Shaken Rogers's Theorem for Homothetic Sections. Canadian mathematical bulletin, Tome 52 (2009) no. 3, pp. 403-406. doi: 10.4153/CMB-2009-043-8
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     author = {Jer\'onimo-Castro, J. and Montejano, L. and Morales-Amaya, E.},
     title = {Shaken {Rogers's} {Theorem} for {Homothetic} {Sections}},
     journal = {Canadian mathematical bulletin},
     pages = {403--406},
     year = {2009},
     volume = {52},
     number = {3},
     doi = {10.4153/CMB-2009-043-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2009-043-8/}
}
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